In this chapter, we discussed the main principles of adversarial training, and explained the roles of two players: the generator and discriminator. We described how to model and train them using a minimax approach whose double goal is to force the generator to learn the true data distribution p_data, and get the discriminator to distinguish perfectly between true samples (belonging to p_data) and unacceptable ones. In the same section, we analyzed the inner dynamics of a Generative Adversarial Network and some common problems that can slow down the training process and lead to a sub-optimal final configuration.

One of the most difficult problems experienced with standard GANs arises when the data generating process and the generator distribution have disjointed support. In this case, the Jensen-Shannon divergence becomes constant and doesn't provide precise information about the distance. An excellent alternative is provided by the Wasserstein measure, which is employed in a more efficient model, called WGAN. This method can efficiently manage disjointed distributions, but it's necessary to enforce the L-Lipschitz condition on the Critic. The standard approach is based on clipping the parameters after each gradient ascent update. This simple technique guarantees the L-Lipschitz condition, but it's necessary to use very small clipping factors, and this can lead to a slower conversion. For this reason, it's normally necessary to repeat the training of the Critic a fixed number of times (such as five) before each single generator training step.

In the next chapter, we are going to introduce another probabilistic generative neural model, based on a particular kind of neural network, called the Restricted Boltzmann Machine.